The Channel is narrow. On a clear day you can see the other side. It's a day trip by landing craft. The trucks drive off fully loaded. No port required. Again there is an article/paper for this. I'm not saying that Log is my Jam, but I have a wargamer's respect for the supply. So when read these things they stick with me.
Good points.
You still have to get them from the Med, where they are, to the Channel where they are not. Not easy. Strait of Gibraltar was a severe problem for underpowered ships (6 knot current.). Trip to Cotentin Pennisula from the invasion ports is;
~ 70 NM at ~ 7 knots (LST average speed) which means 10 hours to a whole day to arrive sea-sick off Sword, Gold, Juno, Omaha and Utah.